| Initial boundary value problem of two dimensional unsteady diffusion equations is solved in this paper. By using time-dependent fundamental solution of two dimensional diffusion equations and the extension of double layer potential, we establish virtual boundary integral expression of diffusion equations. Then virtual boundary element method is used to implement the numerical computation.Virtual boundary element algorithm is based on the discretization of the boundary integral equation on imaginary virtual boundary. Due to field points and source points lay on real and virtual boundary respectively, the singular integration or nearly singular integration is avoided. Meanwhile, this algorithm keeps the general advantages of the standard boundary element method, such as the decrease of dimensional and the computational scale. The traditional virtual boundary integral expression is based on the extension of single layer potential, for the integral formulas related to single layer potential for parabolic problem, the numerical computation of the exponential integral function is unavoidable. In this thesis, the virtual boundary integral equation is based on double layer potential with the virtual density to be determined on virtual boundary. Since this integral equation related to double layer potential only involves the computation of the normal derivative and second normal derivative of fundamental solution, the exponential integral function is not involved in it, so numerical computation for the exponential integral function is avoid. The integration for time is carried out analytically, meanwhile constant elements and equivalent collation method are used for the discretization of virtual and real boundary.Some numerical examples are performed to show the performance of the proposed method. Compared with analytical solutions, the numerical results have the high accuracy. Thus, the proposed method is an efficient method for solving diffusion equation.
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